In layman terms, if a person buys a single share it should have the least impact possible on the price, and if a person buys the entire market's worth of shares the price should theoretically go to infinity. Any Marginal volume purchased should always be positively correlated with price movement upwards. The same goes for selling in the other direction. Any "proprietary trading" algorithm that violates this simple rule IS NOT MARKET MAKING. How simple is that? An algorithm that continuously alters the correlation between volume and price movement is NOT MARKET MAKING. Plus, any application of game theory in market making algorithms is illegal collusion. So the Volcker Rule exception for market making should have very narrow application.
Game theory is when algorithms from different market makers communicate by sending test sells or buys, or the people in charge of them agree ahead of time not to do a shark frenzy sort of thing where they compete with each other such that none of them gets to collect a large profit and instead each only get small ones. Also some "Smart routing" algorithms that route retail orders are also a sort of game theory application, because they break up large orders and ensure on average that all market makers have equal motives in terms of where they want the price to be by equally distributing open interest in options. In short game theory applications are a form of price fixing as if all grocery stores in an area decided to sell apples for 10 bucks each and none of them priced any lower.